ABSTRACT
Let K be a field. A split basic finite-dimensional K-algebra with left quiver Γ is binomial if it can be represented as the path algebra modulo relations of the form
, where
and p and q are paths in Γ. We here characterize all binomial algebras A as twisted semigroup algebras
, where S is an algebra semigroup, and where
is a two-dimensional cocycle of S with coefficients in the multiplicative group of units
of K. Subject to certain conditions on an algebra semigroup S, we classify the twisted semigroup algebras of S up to isomorphism. Finally, subject to the same conditions on S, we show that for each binomial algebra
there exists a short exact sequence